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Difficulty: EasyOrder of Operations and Number Properties

Evaluate the following three mathematical expressions and arrange them in order from least to greatest value.

  1. 14×(2−3)4 \times (2 - 3)
  2. 24−2×34 - 2 \times 3
  3. 3(4−2)×3(4 - 2) \times 3

Answer

The correct order of the expressions from least to greatest value is 4×(2−3)4 \times (2 - 3), followed by 4−2×34 - 2 \times 3, and then (4−2)×3(4 - 2) \times 3.
Evaluating each expression using the order of operations results in values of −2-2, 66, and −4-4. Arranging these values in increasing order yields −4<−2<6-4 < -2 < 6, which corresponds to the sequence 4×(2−3)4 \times (2 - 3), followed by 4−2×34 - 2 \times 3, and then (4−2)×3(4 - 2) \times 3.

Step-by-Step Solution

1
Evaluate the expression 4−2×34 - 2 \times 3.
−2-2
Apply the order of operations (PEMDAS) by performing the multiplication first: 2×3=62 \times 3 = 6. Then perform the subtraction: 4−6=−24 - 6 = -2.
2
Evaluate the expression (4−2)×3(4 - 2) \times 3.
66
Apply the order of operations by simplifying the subtraction inside the parentheses first: 4−2=24 - 2 = 2. Then perform the multiplication: 2×3=62 \times 3 = 6.
3
Evaluate the expression 4×(2−3)4 \times (2 - 3).
−4-4
Apply the order of operations by simplifying the subtraction inside the parentheses first: 2−3=−12 - 3 = -1. Then perform the multiplication: 4×(−1)=−44 \times (-1) = -4.
4
Compare the evaluated values to order them from least to greatest.
−4<−2<6-4 < -2 < 6
Comparing the values reveals that −4-4 is the smallest value, −2-2 is the middle value, and 66 is the largest value.

Key Concept

Order of operations (PEMDAS) requires performing calculations in parentheses first, followed by exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right).
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Topics

Order of Operations and Number Properties

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